Cited by 12,187Fuzzy Logic and Control SystemsAdvanced Algebra and LogicMathematical Control Systems and Analysis

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The concept of a linguistic variable and its application to approximate reasoning—I

Zadeh, L.A.·1975·Information Sciences

DOI 10.1016/0020-0255(75)90036-5

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“According to the fuzzy linguistic approach (Zadeh 1975), the semantics of two adjacent linguistic terms have overlapping parts.”
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“Type-2 fuzzy sets were introduced by Zadeh (1975) and subsequently developed by Mendel and his co-authors (Mendel 2017).”
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“As a consequence, the linguistic variable was developed by Zadeh [21] as a tool to represent qualitative information in decision-making issues.”
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“For instance, the concepts of fuzzy sets and linguistic term sets were introduced by Zadeh [30,31].”
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“…of FST, several extension forms have been developed to suit various decision-making problems, such as intuitionistic fuzzy sets (Atanassov, 1986), type-2 fuzzy sets (Zadeh, 1975), hesitant fuzzy sets (Torra, 2010), and complex linguistic term sets (Gou et al., 2017, 2021a, 2021b, 2023), etc.”
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“1 [50] If k is a natural number and lb denotes a linguistic variable, then T 1⁄4 flb : b 1⁄4 k; .”
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“Besides that, in some complex decision problems where the decision maker (DM) cannot assign MD and NMD to qualitative attributes, a viable option is to express them using linguistic variables (LVs) introduced by Zadeh (1975).”
Background
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“S i and S j should satisfy [18], [50] the following: 1) S i ≤ S j if and only if i ≤ j ; 2) the negation operation neg ( S i ) = S j if i + j = 2 t ; 3) if i ≥ j , then max { S i , S j } = S i ; 4) if i ≥ j , then min { S i , S j } = S j .”
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“[17, 18] are more consistent with Zadeh’s notion [3], but it cannot directly represent the actual decision information; while the domain and range in other deﬁnitions are different from Zadeh’s idea [3] (which is explained thoroughly in Sect.”
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“In the study, each answer on the Likert scale was assigned to a TFN, with no loss of generality [49,50].”
Method
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“Mathematics has successfully explained this phenomenon through the application of fuzzy set theory, which was proposed by Zadeh.22 From the beginning of the fuzzy set, MCDM problems not involving imprecise information have been successfully modeled.”
Method
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“The FN introduced by Zadeh [26] is deﬁned as follows.”
Background
A Hybrid Model Based on SEM and Fuzzy TOPSIS for Supplier Selection
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“Zadeh’s [28] introduction of the concept of linguistic variables allowed calculations to be performed with words instead of numbers; thus linguistic terms deﬁned by fuzzy sets are widely required in various ﬁelds.”
Background
An integrated decision-making methodology based on Pythagorean fuzzy sets for social robot evaluation
Kaya, I., Karaşan, A., Özkan, B., & Çolak, M. (2022) · Soft Computing - A Fusion of Foundations, Methodologies and Applications · doi:10.1007/s00500-022-07303-5 · Cited by 15
“After introducing the fuzzy sets and fuzzy logic, many researchers investigated and worked in the same area and proposed various extensions of the fuzzy sets (Zadeh 1972, 1965, 1975; Grattan-Guinness 1976; Jahn 1975; Sambuc 1975; Atanassov 1986; Smarandache 1995; Torra 2010).”
Method
A New Fuzzy Extension of the Simple WISP Method
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“The weight of each criterion and each sample’s evaluation under uncertainty conditions were described in a positive trapezoidal fuzzy number [40].”
Method
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“When we transform the AIFS in to Zadeh FS, a negative relation should lie between its function and knowledge measure.”
Method
Extending a fuzzy network data envelopment analysis model to measure maturity levels of a performance based-budgeting system: A case study
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Interval type-2 fractional fuzzy inference systems: Towards an evolution in fuzzy inference systems
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A new interval type-2 fuzzy reasoning method for classification systems based on normal forms of a possibility-based fuzzy measure
Kalhori, M. R. N., & Zarandi, M. H. F. (2021) · Information Sciences · doi:10.1016/j.ins.2021.09.060 · Cited by 15
Granulized Z‐OWA aggregation operator and its application in fuzzy risk assessment
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“1 1 (1) 2 1 (2) 1 2 (1) 2 2 (2) 1 3 (1)”
MethodInfluential
Risk assessment of coal and gas outburst in driving face based on finite interval cloud model
Zhang, G., Wang, E., Li, Z.-H., & Qin, B.-S. (2021) · Natural Hazards · doi:10.1007/s11069-021-05021-z · Cited by 15
Linguistic-valued layered concept lattice and its rule extraction
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Pythagorean fuzzy linguistic decision support model based on consistency-adjustment strategy and consensus reaching process
Liu, J.-P., Fang, M., Jin, F.-F., Tao, Z., Chen, H., & Du, P.-C. (2021) · Soft Computing - A Fusion of Foundations, Methodologies and Applications · doi:10.1007/s00500-021-05747-9 · Cited by 15
“Let S ¼ s i i ¼ 1 ; 2 ; . . . j f ; 2 s g be a ﬁnite ordered discrete LTS with odd cardinality (Zadeh 1975; Xu 2005), where the term s i represents a possible value for a linguistic variable and 2 s is a positive integer.”
Background
Multilevel AHP approach with interval type-2 fuzzy sets to portfolio selection problem
Meniz, B., Bas, S. A., Ozkok, B., & Tiryaki, F. (2021) · Journal of Intelligent & Fuzzy Systems · doi:10.3233/jifs-200512 · Cited by 15
“Later, Zadeh [45] further extended the concept of fuzzy sets and introduced type-2 fuzzy sets as an extension to fuzzy sets.”
Adaptive Interval Type-2 Fuzzy Filter: An AI Agent for Handling Uncertainties to Preserve Image Naturalness
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“The proposed AIT2FF is based on the FST introduced by Zadeh [39].”
Method
Second-order neutrosophic boundary-value problem
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“Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning—i. Inf Sci 8(3):199–249 3.”
BackgroundInfluential
A consensus method based on reinforcement learning for group decision-making
Shen, Y.-F., Ma, X.-L., Bao, Y.-K., Kou, G., & Zhan, J.-M. (2025) · European Journal of Operational Research · doi:10.1016/j.ejor.2025.08.054 · Cited by 14
Linguistic Pythagorean fuzzy Aczel-Alsina aggregation operators and their application in multi-attribute group decision-making: An approach for smart city development
Gurmani, S. H., Rasool, Z., Ali, R., Bano, S., Chen, H., Feng, Y., & Zulqarnain, R. M. (2025) · Engineering applications of artificial intelligence · doi:10.1016/j.engappai.2025.111215 · Cited by 14
Tourism attraction selection driven by online tourist reviews: A novel multi-attribute decision making method based on the evidence theory and probabilistic linguistic term sets
Yang, H., & Xu, G. (2025) · Applied Soft Computing · doi:10.1016/j.asoc.2025.113243 · Cited by 14
Selection of artificial intelligence tool for blind assistance based on Dombi aggregation operators for intuitionistic linguistic decision-making problems
Ali, Z., Senapati, T., & Moslem, S. (2025) · International Journal of System Assurance Engineering and Management · doi:10.1007/s13198-024-02683-3 · Cited by 14
“Zadeh (Zadeh 1975a, 1975b) initiated the linguistic variables (LVs) and discussed their application in approximate reasoning.”
Integrating GRA with intuitionistic fuzzy VIKOR model to explore attractive design solution of wickerwork cultural and creative products
Wang, T., Yang, L., & Liu, L. (2025) · doi:10.1080/09544828.2024.2401750 · Cited by 14
“Fuzzy theory was proposed by ZADEH in 1965 (Chai, Zhou, and Jiang 2023) and is suitable for dealing with problems related to uncertainty and ambiguity based on simulating fuzzy human thinking and decision-making processes (Ghosh and Sing 2023; Zadeh 1975).”
Comparative study on deep and machine learning approaches for predicting wind pressures on tall buildings
Kaloop, M. R., Bardhan, A., Samui, P., Hu, J. W., & Elsharawy, M. (2025) · Alexandria Engineering Journal · doi:10.1016/j.aej.2024.10.047 · Cited by 14
Type‐3 Fuzzy System‐Based Intelligent Control Approaches and Applications
Abdalla, T. Y., Abdalla, A. Y., & Chyaid, A. M. (2025) · Advances in Fuzzy Systems · doi:10.1155/adfs/6661495 · Cited by 14
“Later the author in [13] advanced the feld by proposing type-2 fuzzy (T2F) set, for better handling uncertainty.”
Group decision-making method based on Pythagorean fuzzy rough numbers
Akram, M., Fatima, U., & Alcantud, J. (2024) · Journal of Applied Mathematics and Computation · doi:10.1007/s12190-024-02317-8 · Cited by 14
“Zadeh[61] proposed the notion of linguistic variable.”
Dynamic critical factors identification: A novel fuzzy DEMATEL method considering heterogeneous information
Zhang, Z.-X., Wang, L., Xie, X., Wu, Q., Wang, Y., & Rodríguez, R. M. (2024) · Expert Systems with Applications · doi:10.1016/j.eswa.2024.125957 · Cited by 16
Quasirung orthopair fuzzy linguistic sets and their application to multi criteria decision making
Zhao, Z., Ye, J., Rahim, M., Amin, F., Ahmad, S., Asim, M., & Ateya, A. A. (2024) · Scientific Reports · doi:10.1038/s41598-024-76112-7 · Cited by 14
New approach for quality function development based on cooperative game-based consensus mechanism and three-way decision method
Wang, J., Liu, H.-C., Zhang, J.-Y., Shi, H., & Zhang, Q.-Z. (2024) · International Journal of Production Economics · doi:10.1016/j.ijpe.2024.109380 · Cited by 14
Multi-criteria decision-making for the selection of best airport ground access mode with a new fuzzy rough-entropy based method
Akram, Z., Ahmad, U., & Alcantud, J. (2024) · Engineering applications of artificial intelligence · doi:10.1016/j.engappai.2024.108843 · Cited by 14
A self-organizing interval type-2 fuzzy neural network for multi-step time series prediction
Yao, F.-L., Zhao, W., Forshaw, M., & Song, Y. (2024) · Applied Soft Computing · doi:10.1016/j.asoc.2025.113221 · Cited by 14
Enhancing reliability of failure modes and effects analysis dealing with linguistic distribution assessments: A consistency based approach
Jia, X., Wang, Y., & Martínez, L. M. (2024) · Engineering Applications of Artificial Intelligence · doi:10.1016/j.engappai.2024.108333 · Cited by 14
Introduction to q-Fractional Fuzzy Set
Gulistan, M., & Pedrycz, W. (2024) · International Journal of Fuzzy Systems · doi:10.1007/s40815-023-01633-8 · Cited by 14
Multi-criteria constrained interval type-2 fuzzy decision-making: A space analysis perspective
Li, H., Dai, X.-C., Zhou, L.-G., & Yang, W. (2024) · Information Sciences · doi:10.1016/j.ins.2024.120581 · Cited by 14
A Distributionally Robust Fuzzy Optimization Approach for Resilient Manufacturing Supply Chain Network Design: An RCEP Perspective
Cheng, X.-X., Wang, L.-Q., & Wang, J. (2024) · IEEE transactions on fuzzy systems · doi:10.1109/tfuzz.2023.3324207 · Cited by 14
“Proposed by Zadeh [27], the T2F set uses both primary membership values and secondary possibility distributions to deﬁne its membership function, thereby avoiding dependence on exact membership function [28].”
Method
QFD-based hybrid neutrosophic MCDM approach with Six Sigma evaluation for sustainable product design in Industry 4.0
Kar, A., & Rai, R. (2024) · Kybernetes · doi:10.1108/k-09-2023-1757 · Cited by 14
A hybrid traffic controller system based on flower pollination algorithm and type-2 fuzzy logic optimized with crow search algorithm for signalized intersections
Korkmaz, E., & Akgüngör, A. P. (2024) · Soft Computing - A Fusion of Foundations, Methodologies and Applications · doi:10.1007/s00500-024-09643-w · Cited by 14
“The concept of type-2 fuzzy sets is an extension of the concept of type-1 fuzzy sets proposed by Zadeh (1975).”
Triangular intuitionistic fuzzy linear system of equations with applications: an analytical approach
Shams, M., Kausar, N., Agarwal, P., & Shah, M. A. (2024) · Applied Mathematics in Science and Engineering · doi:10.1080/27690911.2023.2299385 · Cited by 14
Let us take a walk to the sustainable tourism practices: a qualitative study through the lens of tourism experts
Arya, V., Auruškevičienė, V., Agarwal, S., Kokatnur, P., Kumar, H., & Verma, R. (2024) · Environmental science and pollution research international · doi:10.1007/s11356-023-31503-7 · Cited by 14
“Then, to distinguish between fuzzy sets and type-2 fuzzy sets, previous fuzzy sets are commonly called type-1 fuzzy sets (Zadeh 1975).”
A novel decomposed Z-fuzzy TOPSIS method with functional and dysfunctional judgments: An application to transfer center location selection
Tüysüz, N., & Kahraman, C. (2024) · Engineering applications of artificial intelligence · doi:10.1016/j.engappai.2023.107221 · Cited by 14
Z-DNMASort: A double normalization-based multiple aggregation sorting method with Z-numbers for multi-criterion sorting problems
Liao, H.-C., Xiao, Y., Wu, X., & Baušys, R. (2024) · Information Sciences · doi:10.1016/j.ins.2023.119782 · Cited by 14
Three-way decisions based on bipolar-valued fuzzy sets over three-way decision spaces
Hu, B.-Q. (2024) · Information Sciences · doi:10.1016/j.ins.2023.119912 · Cited by 14
Solution of Z-number-based multi-objective linear programming models with different membership functions
Akram, M., & Ullah, I. (2024) · Information Sciences · doi:10.1016/j.ins.2024.120100 · Cited by 14
On SIR-based MCDM approach: Selecting a charcoal firm using hybrid fuzzy number on a Triple Vague structure
Rajadurai, M., & Kaliyaperumal, P. (2024) · Heliyon · doi:10.1016/j.heliyon.2024.e24248 · Cited by 14
“Zadeh [7] explained fuzzy set construction which is a signiﬁcant area of mathematics that gives MCDM a foundation for solving such everyday problems in complex situations.”
Background
An Automatic Consensus Reaching Approach With Preference Adjustment Willingness for Group Decision-Making
Huang, T., Tang, X.-A., Zhang, Q., Cai, Z., & Pedrycz, W. (2023) · IEEE transactions on fuzzy systems · doi:10.1109/tfuzz.2023.3250341 · Cited by 14
“First, the numerical preference representation structure (FPR) was used in this study, while in real-world GDMs, DMs tend to use linguistic variable [35] to express their preferences rather than numerical values.”
Method
Group decision-making method based on expert credibility with multi-granularity probabilistic linguistic Z-number preference relation
Zhang, J., & Li, M. (2023) · Information Sciences · doi:10.1016/j.ins.2023.119664 · Cited by 14
Sustainability assessment for construction projects: A cost-sustainability tradeoff approach
Hussain, A., & Hussain, I. (2023) · Journal of Cleaner Production · doi:10.1016/j.jclepro.2023.138727 · Cited by 14
Generalized linear diophantine fuzzy Choquet integral with application to the project management and risk analysis
Riaz, M., Garg, H., Hashmi, M., & Farid, H. M. A. (2023) · Computational and Applied Mathematics · doi:10.1007/s40314-023-02421-8 · Cited by 14
Scores of hesitant fuzzy elements revisited: "Was sind und was sollen"
Alcantud, J., Campión, M. J., Induráin, E., & Munárriz, A. (2023) · Information Sciences · doi:10.1016/j.ins.2023.119500 · Cited by 14
Hesitant picture fuzzy linguistic prospects theory-based evidential reasoning assessment method for digital transformation solution of small and medium-sized enterprises
Wu, X., & Yang, L. (2023) · Complex & Intelligent Systems · doi:10.1007/s40747-023-01125-0 · Cited by 15
Addressing Environmental Protection Supplier Selection Issues in a Fuzzy Information Environment Using a Novel Soft Fuzzy AHP-TOPSIS Method
Chung, H.-Y., Chang, K.-H., & Yao, J.-C. (2023) · Syst. · doi:10.3390/systems11060293 · Cited by 14
“Zadeh [33] proposed a mathematical theory of fuzzy sets, which are extensions of ordinary sets in mathematics.”
BackgroundInfluential
Distance and Similarity Measures of Intuitionistic Fuzzy Parameterized Intuitionistic Fuzzy Soft Matrices and Their Applications to Data Classification in Supervised Learning
Memiş, S., Arslan, B., Aydın, T., Enginoğlu, S., & Camcı, Ç. (2023) · Axioms · doi:10.3390/axioms12050463 · Cited by 16

Authors: Zadeh, L. A.
Affiliations: University of California, Berkeley (US)
Corresponding author: Zadeh, L.A.
Venue: Information Sciences
Publisher: Elsevier BV
Published: 1975
Volume: 8
Issue: 3
Pages: 199-249
ISSN: 0020-0255 (ISSN-L)
DOI: 10.1016/0020-0255(75)90036-5
OpenAlex: W4245152641
Cited by: 12,187
References: 48
Citations by year: 2026: 309 · 2025: 516 · 2024: 569 · 2023: 707 · 2022: 682 · 2021: 746 · 2020: 693 · 2019: 759 · 2018: 655 · 2017: 598 · 2016: 551 · 2015: 546 · 2014: 484 · 2013: 437 · 2012: 367
FWCI: 13.65
Type: journal article
Language: en
Open access: closed
Licence: www.elsevier.com/tdm/userlicense/1.0/ (tdm)
www.elsevier.com/legal/tdmrep-license (tdm)
Locations: Information Sciences (publishedVersion)
Funders: Army Research Office (DA-ARO-D-31-124-7 l-G1 74)
National Science Foundation (GK-VP-610656X3)
Topics: Physical Sciences › Computer Science › Artificial Intelligence › Fuzzy Logic and Control Systems
Physical Sciences › Computer Science › Computational Theory and Mathematics › Advanced Algebra and Logic
Physical Sciences › Computer Science › Artificial Intelligence › Mathematical Control Systems and Analysis
Keywords: linguistic variables, approximate reasoning, fuzzy logic, compatibility function, hedges, linguistic truth values, nonlinear programming, human decision-making, fuzzy sets, artificial intelligence

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